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http://math.stackexchange.com/questi...braic-topology

15. Show that if a connected manifold M is the boundary of a compact manifold, then the Euler characteristic of M is even.
16. Show that $\mathbb{RP}^{2n} $ and $\mathbb{CP}^{2n} $ cannot be boundaries.
17. Show that $\mathbb{CP}^2#\mathbb{CP}^2 $ cannot be the boundary of an orientable 5-manifold.
18. Show that the Euler characteristic of a closed manifold of odd dimension is zero.

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